Fibre Reinforcement in Load Carrying Concrete Structures
Thesis for the degree of philosophiae doctor
Åse Lyslo Døssland
Trondheim, February 2008
Norwegian University of Science and Technology
Faculty of Engineering Science and Technology
Department of Structural Engineering
NTNU
Norwegian University of Science and Technology Thesis for the degree of philosophiae doctor Faculty of Engineering Science and Technology Department of Structural Engineering
©Åse Lyslo Døssland
ISBN 978-82-471-6924-7 (electronic ver.) ISBN 978-82-471-6910-0 (printed ver.) ISSN 1503-8181
Doctoral Thesis at NTNU, 2008:50 Printed by NTNU Trykk
Fibre reinforcement can provide an alternative to conventional steel bars in order to improve the efficiency and working conditions on construction sites and in the prefabrication industry. Through the fibres ability to bridge cracks they improve the structural behaviour of the concrete by increased shear, moment and punching resistance, increased dowel effect, reduced crack spacing and crack widths, increased flexural stiffness and increased ductility in compression. A main reason for limited use of FRC in load-carrying structures seems to be the lack of accepted design guidelines.
The principal aim of this research project is to improve the current knowledge of the mechanical and structural behaviour of fibre reinforced concrete, focusing on practical applications. An experimental study is carried out where the following parameters are investigated: fibre volume, fibre length, steel versus synthetic fibres, size effect, influence of conventional reinforcement, self compacting versus vibrator compacted concrete, casting process and type of structural element.
Most of the test series were evaluated through calculations and finite element analysis (FEA) and compared with available design rules. Generally the agreement was good, both with discrete and smeared crack approach. This shows that FEA is an appropriate tool to determine the contribution of fibres to the load bearing capacity. Moreover, the results of the test series implied that the theoretical framework that exists today describes the behaviour of fibre reinforced structures relatively well, and that the design rules which are developed is satisfactory.
Bruk av fiber som erstatning for vanlig slakkarmering i betongkonstruksjoner er svært aktuelt på grunn av større krav til rasjonell utførelse, samt HMS- forhold for jernbindere og mangel på arbeidskraft. Fiberarmering i plasstøpte betongkonstruksjoner er i Norge i dag hovedsakelig begrenset til stålfiberarmering i golv på grunn og påstøp og i spesialutførelser som sprøytebetong. En viktig årsak til at bruk av fiberarmering er såpass begrenset er at en mangler generelt aksepterte regler for beregning og utførelse av fiberbetong.
PhD prosjektet har hatt som hovedmål å øke kunnskapen om bruk av fiberbetong, både med hensyn på utførelse og dimensjonering. Det eksperimentelle arbeidet har i hovedsak vært finansiert gjennom et utvikingsprosjekt der intensjonen har vært å utvikle retningslinjer for dimensjonering og utførelse av stålfiberarmert betong som igjen kan legges til grunn for godkjenning fra byggherrer og bygningsmyndigheter. I tillegg har PhD prosjektet omfattet syntetiske makro fiber, og følgende forsøksserier er utført:
Heftegenskaper - Uttrekksforsøk
Uttrekksforsøk av enkeltfiber med ulik betongfasthet, innstøpingslengde og fibertype (syntetisk makro fiber, stålfiber med endekroker). Forsøksserien viste blant annet at syntetiske fiber oppnår maks uttrekkskraft med høyere uttrekkslengder enn stålfiber. Det var tydelig at økt betongfasthet forbedret heften mellom fiber og betong. Dessuten understreket uttrekksforsøkene at endekrokene på stålfibrene utgjør hovedbidraget til uttrekksmotstanden.
stålfiberarmert betong. Små bjelker ble saget ut fra elementene og testet for å finne bøyestrekkfasthet og restfasthet etter opprissing. Formålet med forsøksserien var å undersøke fiberorienteringen gjennom elementene.
Spesielt for plata med SKB var orienteringen jevn og gunstig. For de andre elementene viste den store spredningen i resultatene at fiberorienteringen varierte betraktelig. Forsøkene viste dessuten at middelspenningen i fibrene var høyere med SKB enn med vibrert betong selv om fastheten var tilnærmet lik.
Bjelkeprøving - moment og skjærbrudd
16 bjelker med planlagt moment- eller skjærbrudd ble testet. Parametere som ble undersøkt var vanlig vibrert betong kontra SKB, fibervolum, fiberlengde og innflytelse av tradisjonell armering. For momentkapasiteten var effekten av stålfibrene dobbelt så stor for den selvkomprimerende som for den ordinære betongen, noe som skyldes stor ensretting av fibrene i underkant av bjelketverrsnittet. Det var liten forskjell i skjærkapasitet mellom bjelkene med vibrert betong og de tilsvarende bjelkene med SKB. Forsøksresultatene var i god overensstemmelse med dimensjoneringsreglene.
Syntetiske fiber
36 små bjelker ble saget fra vegg og plateelement med ulike fibertyper og konsentrasjoner. Formålet var å sammenligne restfastheten for SKB med syntetiske fiber og SKB med stålfiber. Resultatene viste at syntetiske fiber kan overføre strekkspenninger over betongrissene på samme måte som stålfiber, men siden maksimal spenning blir oppnådd ved høyere rissvidder kan kapasiteten til betong med syntetiske makro fiber kun utnyttes når det blir tolerert relativt høye verdier for maksimal rissvidde.
størrelseseffekt av stålfiberarmert betong. Tre bjelker var armert med 1 % fiber, tre med 0,3 % fiber, og tre var armert både med 1 % fiber og kamstål.
Effekten av økende tverrsnittshøyde på bøyestrekkfastheten tilsvarte vanlig armert betong. For bjelkene med 1 % fiber minket maksimal last og duktilitet relativt til last ved opprissing med økende tverrsnittshøyde.
Plater med punktlast
13 plater med dimensjon 1,2 x 0,15 x 3,6 m fritt opplagte på to render ble pålastet med en punktlast i midten. Formålet var å undersøke effekten av ulike fibertyper og armeringsforhold med hensyn til rissfordeling, duktilitet og maksimal last, og å kontrollere om fibrene kunne overføre lasten fra midten av platen til armeringsstengene som var plasserte nært langsidene av platen.
Resultatene indikerte at maksimum avstand mellom armeringsstengene i henhold til standard dimensjoneringsregler for vanlig betong kan økes ved bruk av fiber. Videre viste fibertelling at fibrene hadde en hovedorientering langsetter platen, noe som tyder på at fibrene hadde rettet seg parallelt med flyteretningen til betongen.
Fiber som skjærarmering i hulldekkelement
12 fritt opplagte hulldekkeelement med dimensjon 4 x 1,2 x 0,32 m ble belastet med en linjelast 800 mm fra opplegg for å undersøke om fibrene kunne øke skjærkapasiteten til elementene. Produksjonsteknisk og med tilslaget som var tilgjengelig viste det seg å være vanskelig å oppnå god komprimering av betongen rundt spennstålet. Konsekvensen var at kapasitetsøkningen var neglisjerbar fordi det oppstod uttrekksbrudd av spenntauene før skjærkapasiteten var oppnådd. Den eneste fordelen med fibertilsetningen var derfor økt duktilitet.
militærleir der hele huset var utført med stålfiberarmert SKB. Forsøkene viste at fiber kan erstatte all tradisjonell armering i lastbærende dekker med relativt korte spenn.
Støpemetode
Fire veggelement av fiberarmert SKB ble støpt med pumpe og neddykket slange ved Contigas elementfabrikk i Moss. Formålet var å prøve om det var mulig å produsere en stabil SKB for pumping med det tilgjengelige tilslaget, å kontrollere om det ville oppstå fiberblokkering i rør/pumpe, og undersøke fiberfordeling og -orientering gjennom veggene. Tre fibertyper ble brukt, to typer stålfiber med endekroker og en type makro syntetisk fiber, og fibervolumet var 0,6 %. I en av veggene ble slangen ført frem og tilbake, noe som resulterte i en mer gunstig fiberorientering. Resultatene viste at fiberkonsentrasjonen minket noe med økende avstand til slangen, noe som indikerer at betongen var på grensen til separasjon. Betongens flyteretning var mer konstant i denne forsøksserien enn for veggelementene som var støpt med tobb gjennom trakt fra toppen av forskalingen.
Forsøk sammenlignet med teori
Resultatene ble evaluert vha håndberegninger og elementanalyser og sammenlignet med tilgjengelige dimensjoneringsregler, og generelt sett var overensstemmelsen god. Dette viser at det teoretiske rammeverket som eksisterer i dag i hovedsak kan beskrive oppførselen til fiberarmerte betongkonstruksjoner godt, og at dimensjoneringsreglene som er utviklet er tilfredsstillende.
First of all I would like to express my sincere gratitude to my supervisor Professor Terje Kanstad for giving me the opportunity to work on this research project. Much appreciation is given for his professional support, permanent encouragement and enthusiasm; always focusing on possibilities and solutions instead of problems and limitations.
The thesis is founded by a Norwegian industrial research project, and I would like to thank all participants for making my experimental study possible:
Bekaert, Contiga, Con-Form, Dr. techn. Olav Olsen, Forsvarsbygg, Norbetong, Norcem, Norconsult, NTNU, Skanska Norge, Sintef, Unicon and Veidekke. Special credit is given to Jørn Injar for taking initiative and enabling all experiments that were performed at Contigas factory in Moss.
The research is partly financed by COIN – The Concrete Innovation Centre – which is a centre for research based innovation with funding from the Norwegian Research Council and industrial partners. The financial support is greatly acknowledged.
I am grateful to all my colleagues in the concrete group at the Department of Structural Engineering at NTNU and the concrete group at SINTEF Technology and Society. In particular Senior researcher Erik Thorenfeldt who contributed with valuable comments to the outcome of the research project, Kåre Johansen for his help and expertise regarding concrete mix design and Prof. Karl Vincent Høiseth for continuous encouragement and for valuable discussions.
The experiments of this study could not have been performed without the help and technical expertise of the laboratory personnel; Helge Rødsjø, Svein
more enjoyable and will be remembered with appreciation.
I would like to express my gratitude to the thesis committee members for their interest on my work. Moreover, I’m thankful to Prof. Joost Walraven for organizing my research stay at TU Delft. A warm thank goes to Eleni Lappa and Petra Schumacher for making my stay in Delft so pleasant and memorable, and also for valuable technical comments.
Special thanks go to Helge Nilsen for giving me a challenging and unforgettable summer job as a concreter when I had just started my civil engineer study. This gave me a foundation and interest for concrete structures which I have benefited from throughout my time as a PhD student.
I want to thank my parents, family and friends for the support they provided.
Ida, Rebekka, Kristian, Marco, Ole, Justin, Katrin, Eivind, Ingunn, Madli, Dag Abel, Ann Karin, Dag, Mona, Kjersti, Ingvild – there were too many to mention on this list, thank you for making my time at in Trondheim a pleasant one.
My final thanks go to my boyfriend Nikolai for his unconditional support, encouragement and patience in the final stage of this work.
Åse Lyslo Døssland February 2008
Abstract Sammendrag Acknowledgements Notations
1 Introduction 1
1.1 Background 1
1.2 Scope of the research 2
1.3 Outline of the thesis 3
PART I: THEORETICAL BACKGROUND
2 Fibre reinforced concrete 5 2.1 General – development and use of FRC 5 2.2 Fibres – material, geometries and physical properties 6 2.3 Concrete mix design of fibre reinforced concrete 7 2.3.1 Concrete mix design - VCC with fibres 7 2.3.2 Concrete mix design – SCC with fibres 7 2.4 Mechanics of crack formation and propagation 11 2.5 Mechanical properties and testing methods 13
2.5.1 Compression 13
2.5.2 Tension 16
2.5.3 Shear 21
2.5.4 Pull-out 22
2.6 Orientation and distribution of fibres 31
2.6.1 Introduction 31
2.6.2 Factors influencing the orientation and distribution 32 2.6.3 Theoretical model for orientation 35
3 Structural analysis 43
3.1 Introduction 43
3.2.2 σ−ε relation 45 3.3 Analytical approaches – design for flexure 48
3.3.1 Multi-layer force equilibrium 48 3.3.2 Non-linear hinge model: σ-w method 49
3.3.3 Yield line design 51
3.4 Shear capacity 53
3.5 Finite Element Method 57
3.5.1 Finite element modelling 57 3.5.2 Discrete crack approach 58
3.5.3 Smeared crack approach 59
3.5.4 Choice of crack model in finite element analyses
of FRC. 61
3.6 FRC in the serviceability limit state 62 PART II: EXPERIMENTAL RESEARCH
4 Pull-out tests 67
4.1 Introduction 67
4.2 Concrete specimens – materials and casting procedure 68
4.3 Test setup 70
4.4 Results 72
4.5 Conclusions 78
5 Steel fibre reinforced self compacting concrete 81 5.1 Advantages and drawbacks with FRSCC compared to
FRVCC 81
5.2 36 beams sawn from wall and slab elements with SCC
and VCC 82
5.2.1 Introduction 82
5.2.2 Concrete and casting 82
5.2.3 Experiments 85
5.2.6 Finite element analysis 94
5.3 Conclusions 97
6 Concrete beams reinforced with steel fibres and bars 99
6.1 Fibres as additional reinforcement 99 6.2 Experiments: SFRC beams with VCC and SCC designed for moment and shear failure 99
6.2.1 Introduction 99
6.2.2 Reinforcement 101
6.2.3 Concrete and casting 102 6.2.4 Instrumentation and test setup 105
6.2.5 Results - beams designed for moment failure 107
6.2.6 Design load - beams designed for moment failure 110 6.2.7 Distribution and orientation of fibres – moment beams 116
6.2.8 Results - beams designed for shear failure 120
6.2.9 Design load – beams designed for shear failure 123
6.2.10 Finite Element Analysis 124
6.3 Conclusions 133
7 Synthetic macro fibres 135
7.1 Advantages and limitations of synthetic fibres in load carrying structures 135
7.1.1 Background and range of application 135
7.2 Experiments - Beams sawn from wall and slab elements of FRSCC 136
7.2.1 Introduction 136
7.2.2 Concrete and casting 137
7.2.3 Results 141
7.2.4 Orientation and distribution of fibres 149
7.2.5 Conclusions 152
8.2 Experiments – effect of cross section height for
different reinforcement conditions 156
8.2.1 Introduction 156
8.2.2 Concrete and casting 157
8.2.3 Test setup and instrumentation 159
8.2.4 Results 160
8.2.5 Orientation and distribution of fibres 164
8.2.6 Finite element analysis 165
8.2.7 Conclusions 173
9 Slabs exposed to bending 175
9.1 Introduction 175
9.2 Simply supported slabs with FRSCC exposed to concentrated loads 175
9.2.1 Experiments 175
9.2.2 Reinforcement 176
9.2.3 Concrete and casting 178
9.2.4 Instrumentation and test setup 180
9.2.5 Results 182
9.2.6 Orientation and distribution of fibres 185
9.2.7 Finite element analysis 191
9.2.8 Conclusions 195
10 Field tests 199
10.1 Steel fibres as shear reinforcement in prestressed hollow core units 199
10.1.1 Shear failure in hollow core cross-sections 199
10.1.2 Experiments 201
10.1.3 Results 204
10.1.4 Orientation and distribution of fibres 207
10.1.5 Experience and conclusions – hollow core units 210 10.2 House of SFRC, full scale testing of slabs with SFRSCC 211
10.2.3 Full scale experiment – loading of slabs. 218
10.2.4 Finite element analysis 221
10.2.5 Fibre counting on drilled out cores from the slabs 223
10.2.6 Results 223
10.2.7 Conclusions – house with FRSCC 226
10.3 Casting methods and fibre orientation - FRSCC walls cast with tube 227
10.3.1 Introduction 227
10.3.2 Concrete and casting 228
10.3.3 Beam tests 231
10.3.4 Results 232
10.3.5 Conclusions – wall elements 235
10.4 Conclusions 237
11 Conclusions 239
11.1 Summary and conclusions 239
11.2 Final conclusions and future perspective 244
12 References 245
Appendix
Roman Capital Letters
Ac Concrete cross section [mm2]
Af Area of the cross-section of a single fibre [mm2]
As Steel cross-section [mm2]
Asv Stirrup cross-section [mm2]
Ec E-modulus of concrete [N/mm2]
Es E-modulus of steel [N/mm2]
F Force [kN]
Fa Anchorage capacity (pull-out model) [kN]
Fmax Maximum force [kN]
Fu Load at failure [kN]
Gf Fracture energy of concrete [mm]
L Member length [mm]
Ld Damage zone length [mm]
M Moment [kNm]
Mcr Cracking moment [kNm]
Mmax Moment at maximum load [kNm]
ML Plastic moment [kNm]
N Normal force [kN]
Nf Number of steel fibres per unit area. [-]
V Shear capacity [kN]
Vc Contribution of concrete to the total shear capacity [kN]
Vs Shear contribution from stirrups [kN]
Vf Shear contribution from fibres [kN]
Wf Fibre content [kg/m3]
Roman Lower Case Letters
a Shear span [m]
b Width of cross-section [mm]
bw Minimum width of cross-section [mm]
c Clear concrete cover on the bar [mm]
d Effective height of a cross-section [mm]
df Fibre diameter [mm]
e Eccentricity [mm]
fbf Bonding strength for fibres (pull-out model) [N/mm2]
fc Concrete compressive strength [N/mm2]
fc* Concrete compr. strength at the most compressed side (CDZ model) [N/mm2]
fsy Yield strength of steel [N/mm2]
h Height of cross-section [mm]
hcr Crack band width [mm]
k Proportionality factor [-]
kn Factor to determine characteristic values depending on number of tests [-]
l Span [mm]
lf Fibre length [mm]
n Number of cracks [-]
pe Size factor [-]
s Bar spacing [mm]
srm Average crack spacing [mm]
sn Standard deviation [-]
vf Volume ratio of fibres [-]
w Crack width [mm]
wc Localized deformation (CDZ model) [-]
x,y,z Cartesian coordinate system [-]
Greek letters
α Fibre orientation factor [-]
αfd Filling degree (CDZ model) [-]
β Share of uni-directed fibres [-]
ε Strain [-]
ε0 Strain at maximum stress (CDZ model) [-]
εc Compressive strain [-]
εs Tensile strain [-]
εel Elastic strain [-]
εin Inelastic strain [-]
εs Steel strain [-]
φ Reinforcement diameter [mm]
η Factor which indicates how much of the fibre forces that acts in one direction
[-]
λ Ratio between fibre length and diameter lf/df [-]
ρ Reinforcement ratio [-]
ρf Section ratio of fibres [-]
σ Stress [N/mm2]
σf,average Average stress in fibres [N/mm2]
σc Concrete compressive stress [N/mm2]
σf Fibre bridging stress [N/mm2]
σs Steel stress [N/mm ]
τ Shear resistance [N/mm2]
ω Share of plane-orientated fibres [-]
1.1 Background
Fibre reinforcement can provide an alternative to conventional steel bars in order to improve the efficiency and working conditions on construction sites and in the prefabrication industry. Although fibres most often are used for non-structural applications to control plastic and drying shrinkage, they can also be applied to reduce or in some cases even replace ordinary reinforcement bars. The labour cost makes roughly 40% of the total cost of a concrete building [Löfgren, 2005], where a main part is related to the reinforcement work. The reduced labour can in some cases offset the increased material costs when fibres are used as replacement for conventional bars, especially in Norway where the recruitment of construction workers is particularly low. Moreover, the physically hard reinforcement work often leads to health complaints and an early retirement age. Fibres combined with self compacting concrete (SCC) is furthermore a very promising concept which improves the working conditions further, both with respect to efficiency and to health and safety benefits, since the heavy and noisy vibration work is avoided.
From a structural aspect, the main reason for adding fibres is to improve the fracture characteristics and structural behaviour through the fibres ability to bridge cracks. Fibre bridging over the cracks leads to increased shear, moment and punching resistance, increased dowel effect, reduced crack spacing and crack widths, increased flexural stiffness and increased ductility in compression.
The use of fibre reinforcement for structural applications is in Norway mainly limited to slabs on ground and sprayed concrete for rock support.
Although extensive research has been done over the years to evaluate the
effect of fibres, existing standardised tests and design methods have not always been consistent in its treatment. A main reason for limited use of fibre reinforced concrete (FRC) in load-carrying structures seems to be the lack of accepted design guidelines. A more general utilization of fibre reinforced concrete in structural concrete structures require more detailed design rules, combined with guidance regarding choice of fibre types, concrete composition, execution rules and test methods.
1.2 Scope of the research
The principal aim of this research project is to improve the current knowledge of the mechanical and structural behaviour of fibre reinforced concrete, focusing on practical applications. An experimental study is carried out, and the results are compared with available design rules and with finite element analysis. Further, the connection between casting method and fibre orientation is investigated, since the behaviour of fibre reinforced structures strongly depends on the orientation and distribution of fibres.
The experimental investigations in this thesis are financially supported by the Norwegian industrial research project ”Industrialisation of cast in place concrete – Steel fibre reinforced concrete”, chaired by the contractor Veidekke ASA. This has been a Norwegian joint programme with 14 partners (Consultants, material suppliers, contractors, building owners, government agencies, universities and research institutes), with the main objective to develop nationally accepted guidelines for design and execution of fibre reinforced structures. Hence, a secondary objective of the experimental program has been to support these design guidelines.
1.3 Outline of the thesis
A theoretical background for this work is given in chapter 2 and 3 while the experimental study is presented in chapter 4 to 10. Chapter 2 describes fibre characteristics, concrete mix design and also the mechanics of crack propagation. Moreover, a summary of mechanical properties and testing methods is presented, considering compressive, tensile, shear and pull-out behaviour. Fibre orientation and fibre distribution is also treated, including both theoretical orientation models and fibre orientation in practice; the latter by describing the factors which imposes a pronounced fibre orientation in a particular direction. A number of approaches are available for structural analysis of fibre reinforced concrete both in the ultimate and in the serviceability limit state. Chapter 3 describes some of these methods considering both flexural and shear design and also including finite element modelling. Further, design methods for fibre reinforced concrete in the serviceability limit state are reviewed.
A series of pull-out tests is presented in chapter 4, where three main factors are investigated; compression strength, fibre type and cast in length.
Chapter 5 focuses on fibre orientation based on bending tests on beams sawn from different structural elements made with vibrator compacted concrete (VCC) and self compacting concrete (SCC). Chapter 6 studies the effect of steel fibres on the shear and flexural behaviour based on four point bending tests on beams made with VCC and SCC. A comparison with different available design rules are presented together with finite element analyses. In chapter 7 the influence of synthetic fibres and steel fibres on the flexural behaviour is compared, and size effect of fibre reinforced concrete beams is treated in chapter 8. Chapter 9 examines the effect of different fibre types and reinforcement ratios in slabs exposed to concentrated loads, particularly in order to control if fibres are able to transfer large stresses which enables increased maximum spacing between reinforcement bars. Chapter 10 presents the results of three different field tests. Firstly, steel fibres are used as shear reinforcement in prestressed
hollow core units. Secondly, full scale load testing is carried out on three slabs in a fibre reinforced concrete building. The last field test covers a series of SCC walls cast with tube, with the objective to study the connection between casting method and fibre orientation. Chapter 11 summarises results and experiences gained from the experimental study and presents the final conclusions.
Chapter nr
Parameters 4 5 6 7 8 9 10.1 10.2 10.3
Compression strength x (x)
Fibre volume x x x x x x
Fibre length x x x x x
Steel versus synthetic x x x x
Size effect x
Influence of reinfo. bars x x x x
SCC versus VCC x x
Casting process x x x x (x) x
Type of structural element x x
Figure 1.1: An overview of parameters investigated in the experiments, which are described in the following chapters: 4. Pull-out tests, single fibres. 5. Beams sawn from plates and walls with VCC and SCC. 6. Beams designed for moment- and shear failure (VCC/SCC). 7. Synthetic/steel fibres, beams sawn from wall/plate elements. 8. Scale effect. FRC beams with different cross-section heights. 9. Simply supported slabs (fibres + bars) with concentrated load. 10.1. Prestressed hollow core elements with steel fibres. 10.2. Full scale loading on three slabs in FRC building. 10.3.
SCC wall elements cast with tube.
2 Fibre reinforced concrete
2.1 General – development and use of FRC
Research on fibre reinforced concrete has been conducted since the 1960’s [Shah and Skarendahl 1985]. During the 1970s the commercial use of this material began to increase, particularly in Europe, Japan and USA [Clarke, Vollum et al. 2007]. Common application areas today are shotcrete, pavements, industrial floors, precast elements and various kinds of repairs [Carlswärd 2006].
The addition of randomly distributed steel fibres increases the cracking resistance of concrete, i.e. the fracture toughness, ductility, impact resistance, fragmentation and spalling resistance [Shah and Skarendahl 1985]. However, since fibres generally are distributed through the cross section it is not possible to achieve the same area of reinforcement with fibres as with conventional bars. Hence, for normal fibre contents, the concrete exhibits a softening response.
Fibres are primarily used as replacement for conventional reinforcement in non-structural applications in order to control early thermal contraction cracking and drying shrinkage cracking. However, the use of fibres for structural applications as part of the overall structural design is continuously increasing. In some types of structures with relatively low reliability levels for structural safety such as slabs on grade, foundations and walls, fibres can replace ordinary reinforcement completely.
Furthermore, in load carrying structures in general, fibre reinforcement may be used in combination with conventional or prestressed reinforcement.
Although economical issues has been the main limiting factor for practical use of SFR, it is presently a more interesting alternative due to lack of
skilled concrete workers and need for industrialisation of the construction industry [Kanstad & Døssland 2004].
2.2 Fibres – material, geometries and physical properties
A wide range of fibre types exists, which are made of different materials and with various geometries. Some types of fibres are mainly used to improve the toughness and reduce crack widths, while others are used to reduce plastic shrinkage cracking or to avoid spalling of concrete during fire [Löfgren 2005]. Commonly used materials are steel, glass, carbon, polyvinyl alcohol (PVA), polypropylene, (PP) and cellulose. The fibres come in many different shapes and sizes; PP-fibres can for instance be twisted, fibrillated or monofilament. Macro fibres are often characterized by their aspect ratio, i.e the length to diameter (or equivalent diameter) ratio. Most steel fibres are round in cross-section with diameters between 0.4 and 0.8mm and lengths ranging between 25 and 60mm [Clarke, Vollum et al. 2007]. The draft BS EN 14889-1 [British Standard institution 2006]
classifies steel fibres into fibre groups as follows:
Group I Cold-drawn wire Group II Cut sheet
Group III Melt extract
Group IV Shaved cold drawn wire Group V Milled from blocks
To enhance the bonding between fibre and concrete matrix, the fibres are often deformed, i.e. by end-hooks or end knobs, or they can be crimped (wave shaped) or twisted.
This work focuses on fibres used for structural applications, and for this purpose slender high strength steel fibres are considered to be most efficient. Further, synthetic fibres are becoming more attractive since they can offer similar post-crack ductility to steel fibres.
2.3 Concrete mix design of fibre reinforced concrete
2.3.1 Concrete mix design - VCC with fibres
Fibres affect the workability of the concrete, and at high fibre dosages it is often necessary to increase the filler content or the sand-to-coarse aggregate ratio in the mix composition in order to obtain an optimum packing density. If the maximum fibre volume is reached for a maximum grain size and aspect ratio, the probability for fibre balling increases.
Moreover, the volume of coarse aggregate should not be too high compared to the total aggregate volume.
The mix design of SFRC can be based on the same volume design procedures as for plain concrete, where the fibres are considered as additional coarse aggregates in the mixture. With fibres, a larger internal surface needs to be moistened by cement paste, thus it is recommended to increase the cement weight in SFRC compared to plain concrete.
Consequently, the surface area of the relevant fibre type should be considered in the design phase. Moreover, limiting the maximum grain size improves the workability and decreases the probability of fibre clustering.
[Kooiman, 2000].
2.3.2 Concrete mix design – SCC with fibres
Self compacting concrete (SCC) is flowable and fills formwork and densely reinforced areas without vibration. With fibre reinforced SCC, further improvements can be obtained with respect to working conditions, time-saving and reduced labour costs. However, extended preliminary investigations are often required as regards to mix design.
The slump flow decreases with increasing fibre volume and fibre length [Groth 2000a]. Similar to VCC, adjustments in the mix design can be done to account for fibres, and most often it is necessary to carry out test mixes
to ensure that the concrete maintain self compactability. The components of fibre reinforced self compacting concrete (FRSCC) have to be homogenously distributed to avoid sinking particles, fibre clustering and blocking [Grünewald 2004], and it is important to aim at a smooth grading curve without gap grading [Thorenfeldt, Fjeld et al 2006].
Nemegeer [1999] studied the passing ability of FRSCC with the J-ring in combination with the slump flow test in order to determine the bar spacing required to avoid blocking. He found that a bar spacing of about two times the fibre length was required to avoid blocking. The recommendations for bar-spacing proposed by Groth [2000b] also include the aspect ratio and the volume of fibres. However, the composition of the FRSCC was not considered [Table 2.1].
s/lf Lf/df [-] Max mf [kg/m3] 80 30
≥3
65 60 65 30
≥2
45 60
≥1.5 45 30
Table 2.1: Guidelines for assessment of blocking of SFRSCC where s=(minimum) gap distance between re-bars, lf=fibre length, df=fibre diameter and mf=fibre amount. [Groth 2000b]
Grünewald carried out an extensive study to optimise the mixture composition of FRSCC. The following criteria were applied to judge the self-compactability; a slump flow larger than 600mm, no segregation of the fibres, and a homogenous distribution of FRSCC on the flow table. In the study, 11 reference mixes with maximum aggregate size of 16mm were composed according to the Japanese method [Okamura and Ouchi 1999], proportioned at the upper level of self-compactability. Different fibre types were tested, and the maximum fibre contents obtained were 140, 100, 60
and 60 kg/m3 for Dramix 45/30, Eurosteel 50/50, Dramix 65/40 and Dramix 80/60 respectively. With lower maximum aggregate sizes, even higher maximum fibre contents were reached. However, the study indicated that although the maximum fibre content depends on the mixture composition, the upper limit is a fibre characteristic, which for instance results in an upper limit of 80kg/m3 for Dramix 80/60.
The results were calibrated with a method for predicting the maximum fibre content based on the CBI concept ‘risk of blocking’ [Peterson et al.
1998]. With the CBI method, the minimum amount of paste is calculated based on the aggregate’s grading curve, its nature (natural or crushed) and by using a “risk curve”, where the “risk of blocking” has to remain below 1:
Risk of blocking :
1 1
n n 1
ai ai
i abi i abi
n V
n V
= =
= ≤
∑ ∑
where nai = aggregate contribution of group i to blocking [-]
nabi = blocking volume ratio of group i [-]; nabi=Vabi/Vt
Vt = total volume of the concrete mix [m3] Vai = aggregate volume of group i [m3]
Vabi = blocking volume of aggregate group i [m3]
Further, the blocking volume ratio nabi is determined as a function of the bar spacing to fraction diameter of the aggregates c/df.
In Grünewald [2004] the CBI concept was adjusted by replacing the bar spacing to aggregate fraction diameter ratio c/df with the ratio of fibre length Lf to aggregate fraction diameter. The experimental study lead to maximum fibre factor (vf·Lf/df)max:
Maximum fibre factor= (0.781-MFC)/0.211
where the maximum fibre content (MFC) depends on the kind of aggregates (crushed or nature), the volume of each fraction and the fibre length.
1 , 1 ,
n n
ai ai
i a mfi i a mfi
n V
MFC=
∑
= n =∑
= VThe contribution of aggregate group i to the maximum fibre content (nai) is equal to the volume of each fraction (Vai) and has to be divided by the blocking volume (Va,mfi) which is equal to the MFC-ratio na,mfi. The characteristic points of na,mfi were varied to obtain a high correlation with the experimental results on the maximum fibre factor [Figure 2.1]. Hence, the content and distribution of the aggregates determine the maximum fibre content.
0 0,2 0,4 0,6 0,8 1
0 5 10 15 20 25
LfDaf [-]
na,mfi [-]
Figure 2.1: Relation between the ratio fibre length to equivalent aggregate diameter Lf/Daf and the MFC-ratio na,mfi. [Grünewald 2004]
In addition to the filling ability, Grünewald found that steel fibres affect the passing ability and segregation resistance significantly. The required bar spacing for non-blocking was increased with increasing fibre content.
Hence, to optimise the mixture composition of FRSCC, the filling ability and segregation resistance have to be balanced and the geometrical effect of the fibres on the packing density has to be taken into account.
[Grünewald and Walraven 2003], [Grünewald 2004] and [Grünewald and Walraven 2005].
1.8/0.8 14/0.81 300/0.96
2.4 Mechanics of crack formation and propagation
The main benefit of fibres is their ability to transfer stresses across a crack, and consequently enhancing the toughness and ductility of the concrete as well as the absorption capacity under impact [Clarke, Vollum et al. 2007].
Concrete is a heterogeneous material with pores and micro-cracks caused by shrinkage and thermal strains, which have been restrained by coarse aggregates and boundary conditions. During loading, the matrix transfers part of the load to the fibres before any macro-cracks are initiated. Hence, it is theoretically possible to increase the strength of the material by adding fibres. Yet, for the relatively limited fibre volumes that usually are added to conventional concrete, the fibre reinforcement does not cause any pronounced improvement of strength. This is related to the low tensile strain capacity of the cementitious matrix and also to the increased porosity that the fibre addition may induce. [Löfgren 2005]
Provided that fibre rupture is avoided (depending on the tensile strength of the fibres) debonding between fibre and concrete starts on the shortest embedded lengths until full debonding occurs. The initial micro cracks will then start to grow and eventually lead to a macro crack which covers several micro cracks [Kooiman 2000]. The bridging of fibres across cracks provides a post-crack tensile strength to the concrete as illustrated in Figure 2.2. In addition to debonding and fibre pull-out, other mechanics like matrix spalling and plastic deformation of the fibre might be present, which will be discussed further in chapter 2.5.4. A detailed overview of the mechanics of crack formation is given by Löfgren (2005).
Figure 2.2: Schematic description of the stress-crack opening relationship for plain concrete and for FRC [Löfgren 2005].
Depending on the amount of fibres crossing the crack and on the fibre- matrix bonding, the post-crack stress can be larger than the cracking load, resulting in a so called strain hardening behaviour where multiple cracking occurs [Figure 2.3]. However, for normal fibre dosages (<1%) the material exhibit strain softening behaviour, i.e the damage localises immediately after initiation of the first crack.
Figure 2.3: Definition of high performance fibre reinforced concrete [Kooiman 2000].
2.5 Mechanical properties and testing methods
Different test methods are available to estimate the mechanical properties of fibre reinforced concrete. The reliability of the methods described in this section is dependent on whether the difference in fibre orientation between specimen and structure are accounted for, since the wall-effect can be pronounced in the test specimens. The influence of wall-effect is primarily depending on the relation between fibre length and specimen size. Other aspects that influence the reliability of the methods are production and storage of specimen. One example regarding production of specimens for bending tests is given in Figure 2.4, which illustrates recommend casting methods aiming on avoiding weakness zones with unfavourable fibre orientation.
Figure 2.4: Filling method of beam specimens for FRVCC and FRSCC [Grünewald 2004].
2.5.1 Compression
Moderate concentrations of fibres do not influence the compressive strength significantly. However, fibre addition causes a less brittle failure.
Failure of concrete in compression is related to failure in tension, as tensile stresses act perpendicular to the direction of the compressive load. The tensile stresses cause growth of the pre-existing micro cracks in the concrete, which eventually are bridged by mortar cracks as the stress continues to increase. [Schumacher 2006]
In a fracture mechanics based Compressive Damage Zone (CDZ) model proposed by Markeset (1993), the failure is distinguished into two modes.
After reaching a stress of 0.75fcc, longitudinal cracking is initiated in a limited part of the specimen, the so-called damage zone. The second failure mode occurs after reaching the tensile stress, when lateral deformations within the longitudinal tensile cracks forms a shear band as the adjoining parts start sliding relative to each other. The effect of fibres in the presence of cracks is mainly based on preventing these lateral deformations, which results in a more ductile response [Kooiman 2000].
Figure 2.5: The CDZ model for plain concrete in uni-axial compression [Markeset, 1993]
The CDZ model is a constitutive macro-mechanical model which can be used to calculate the stress-strain relation of concrete in compression. The model has also been extended for additional confinement of the compressive zone with stirrup reinforcement. An overview is given in Schumacher (2006). Based on her research, Schumacher also proposed an extended CDZ model to steel fibre reinforced self-compacting concrete (SFRSCC).
Point σ ε
1 0 0
2 (2αfd-1)fc* (2αfd-1)fc*/Ec
3 fc*
ε0
4 fc* ε0 + Δε
5 0 (ε0-fc*/Ec)ּ(1+2αfdk·Ld/L) +wc/L+Δε
Figure 2.6: Average stress-strain relationship in the extended CDZ model by Schumacher (2006).
All points in Figure 2.6 can be calculated from the following parameters:
Filling degree αfd = 0.9 for NSSCC
Nominal compression strength fc*= fc-1430(e/h)2+380(e/h) Youngs modulus Ec= 0.9 · 9500fc*(1/3)
Strain at maximum stress ε0 = 0.7fc0.31·0.8 - 7.5(e/h)2 + 4.7e/h Proportionality factor k = 3.5 + 10Vflf/df + 60e/h
Localized deformation wc = 0.7 for NSSC
Damage zone length/total length Ld/L = 0.8 - 0.2Vflf/df - e/h
These parameters are determined by curve-fitting from several series of deformation-controlled compressive tests described in Schumacher (2006).
Here e/h is the eccentricity versus cross section height, Vf the fibre volume and lf/df the fibre length/diameter. The additional strain Δε takes into account confinements provided by stirrup-reinforcement or other boundary conditions. In her beam experiments, Schumacher accounted for the confining action of the loading platen in the region with the maximum moment by adding a strain Δε and by increasing the concrete compressive strength.
5
ε·Ld/L+wc/L εin εel ε
ε0
Δε σ
1 2
3 4
fc*
The compressive strength for FRC can be determined by simple standard tests, either on concrete cylinders or cubes [RILEM 2003]
2.5.2 Tension
The fibres influence the tensile behaviour of the concrete. It is mainly the ductility which is affected, not the tensile strength, and the influence is strongly dependent on the fibre content and fibre type. For engineered cementitious composites (ECC), the fibre concentration can be large enough to increase the tensile strength considerably, but for the moderate fibre content that can be applied in ordinary concrete the effect on the peak stress can be neglected.
Figure 2.7: Typical tensile behaviour for SFRC. The value of the post- crack stress after cracking is called the residual strength fftk,res. Different approaches exists for modelling the post cracking stress.
It is when concrete is exposed to bending that the fibres come fully into effect as the softening response leads to a redistribution of stresses which imposes a new state of equilibrium across the cross-section after cracking.
As a result, the maximum moment capacity may exceed the maximum moment of plain concrete [Kooiman 2000].
Uni-axial tensile test
The post-crack response of strain softening FRC can be determined directly in terms of stress-crack opening relation with the uni-axial tensile tests (UTT) as described in the recommendations by RILEM (2001). This test is
fftk,res
ft
ε σ
conducted as a displacement controlled tensile test on a notched cylindrical specimen where both ends are fixed with respect to rotation. However, the applicability of this test method is relative low due to the complex test setup. The uni-axial tensile test is time-consuming and difficult to carry out, and it demands highly trained and experienced personnel. It is therefore more economical to determine the post-crack indirectly by bending or splitting-tests without compromising on the reliability of the method. The uni-axial tensile test is ideal for determining the basic σ−ω relationship which is used in advanced design procedures. For development work on fibres and for assessing the influence of fibre type and dosage the beam test is more suitable [Clarke, Vollum et al. 2007].
Three point bending test
In the three-point bending test (3PBT) proposed by RILEM (2002), the tensile behaviour is evaluated in terms of the load bearing capacity at a certain deflection or crack mouth opening. Notched beams of dimensions 150x150mm cross-section with a minimum length of 550 mm are used as standard test specimens [RILEM 2002]. The advantage of the notch is that the crack forms in a predefined position and not in the weakest section.
Consequently, notched beam tests tend to give higher values of flexural strength than un-notched beam tests but with a higher coefficient of variation [Clarke, Vollum et al. 2007].
Wedge splitting test
In the wedge splitting test (WST) a cube or cylinder is split from one side by a wedge. The load is applied in a deformation controlled way, and the crack opening displacement is measured on top of the specimen. The method does not require sophisticated test equipment. The UTT, WST and 3PBT were compared in a study carried out by Löfgren (2005). It was found that the scatter of the WST was somewhat lower than for the two other methods, although the scatter in general was large for all methods.
This can mainly be explained by the variation in number of fibres crossing the cracks [Löfgren 2005]. Despite the fact that the test method is time- and cost-efficient with good reproducibility, it is still not widely applied.
Figure 2.8: Test setup for the uni-axial tensile test (UTT) [Rilem 2001], three point bending test (3PBT) [Kooiman 2000] and wedge splitting test (WST) [Van Mier 1997]
Four point bending test
The JCI bending test is used in the design guidelines for Dramix steel fibres [Nemegeer 1997] and a corresponding method is also recommended by the Norwegian design rule draft [Thorenfeldt et al. 2006]. In this test, 150 x 150 x 600 mm long un-notched beams are loaded to failure under four point bending across a span of 450mm as illustrated in Figure 2.9. A constant bending moment occurs in the section between the two upper point loads. The deflections in the middle are measured and from this the toughness and the equivalent flexural strength can be calculated.
The advantage with the four point un-notched bending test is that it incorporates the effect of variation in the material’s strength [Kooiman 2000] since the first crack will appear at the weakest section. One disadvantage is that the position of the crack cannot be predicted, which makes it hard to measure the crack opening deflections.
Figure 2.9: 4-point bending. Rig for deflection measurements. L=450mm, d=150mm, b=150 [Thorenfeldt et al. 2006]
In this thesis, the four point bending test is used to determine the tensile behaviour, based on the recommendations in the Norwegian design rule draft. The load is applied with a constant deformation rate at 0.1 mm/min.
The residual strength after cracking is taken as fres=0.37ft,eq, where fft,eq is the average equivalent bending strength recorded between 0.5 and 2.5mm deflection:
fft,eq= F(δ12)L/(bd2)
where L, b and d is given in Figure 2.9 and F(δ12) is the average load between the deflections δ1=0.5 and δ2=2.5 mm which can be calculated from the area under the load-deflection curve in this interval. The factor 0.37 expresses the difference between the tensile stress in the uncracked section and the equivalent tensile stress in the cracked section. This is based on the assumption that the depth of the compressive zone in the cracked stage is 1/10 which results in a ratio between the section modulus in the uncracked and cracked state of 0.37 [Kooiman 2000].
The fibre orientation is considered by cutting a block from the beam specimen and counting the fibres crossing the cross-section. The block is taken from the middle part of the beam between the twin loads at a minimum distance from the crack of 2/3lf, where lf is the length of the fibre.
L/2 L/2 b
d/2
Fibre counting is done on both sawn sections on the block (corresponding to the longitudinal direction of the beam), and the average value is taken.
The method is based on test specimens sawn from plate- or wall elements, depending on the structural elements in which it is intended to use fibre reinforcement. The advantage is that wall effects are reduced, i.e. the fibres tendency to orientate parallel to the walls of the formwork, and that the test results are more representative for the real structure. A drawback of the method is cut-off fibres on the sides of the beams which have reduced pull- out resistance due to reduced anchorage as illustrated in Figure 2.10. The estimated fibre orientation based on fibre counting on sawn-out blocks does not consider that some fibres may be ineffective due to reduced anchorage.
Figure 2.10: Sawn surface – example of cut-off fibres without anchorage.
Testing of sprayed concrete [EN 14488 2006]
To determine the flexural behaviour of fibre reinforced sprayed concrete, special testing methods exists. According to the European Standard [EN 14488 2006] the flexural strengths (first peak, ultimate and residual) are determined by 4-point bending of specimens with dimensions 125 x 75 x 550, and the energy absorption capacity is determined from FRC slab specimens. [Figure 2.11] The loads are applied at a rate of 0.25 and 1.0 mm/min for the beam and slab respectively, and the flexural behaviour is determined from the load-deflection curves. It should however be noted that it is not recommendable to characterize FRC by its energy absorption only, since it does not relate the contribution of fibres to crack widths or
deflections. Especially if synthetic fibres are used it should be considered that the maximum pull-out resistance might be reached at relatively large crack widths.
Figure 2.11: Loading of test specimen for testing of sprayed concrete according to EN 14488.
2.5.3 Shear
Fibres can be used as shear reinforcement as a replacement of stirrups in beams and similar structural applications. Numerous tests have indicated that the addition of steel or synthetic fibres significantly increase the shear strength of concrete structures and transform the failure mode from a
100
600
600 500 450 150
75 150 150
125
:flexural strengths - 4point bending
:energy absorption - slab specimen 100
100
steel plate for loading
brittle-fracture to a more ductile one [Voo and Foster 2006]. As soon as the matrix cracks, the fibres are activated, resulting in a pronounced toughening behaviour due to fibre pull-out [Löfgren 2005]. The shear transfer capacity can be significantly increased, depending on fibre quantities [Barrigan 2002]. Moreover, the punching shear resistance can be increased considerably with fibres [Shaaban and Gesund 1994].
Determining the shear behaviour of fibre reinforced concrete is challenging due to the large number of parameters involved, e.g. shear span to depth ratio, scale effect, type of fibre, fibre content and orientation, bonding between fibre and concrete and also contribution from any longitudinal reinforcement bars placed to sustain high flexural moments [Uomoto et al.
1986]. Several methods exist for determining the shear capacity. The post- crack shear resistance is often based on post cracking tensile stresses determined from uni-axial tensile tests [e.g. Casanova (1997)], or equivalent post-crack flexural strengths determined from standardized beam tests [e.g. Nemegeer 1996, RILEM 2003]. Different methods for determining the shear capacity will be presented and discussed in section 3.4.
2.5.4 Pull-out
After cracking, the fibres transmit tensile stresses over the crack into the surrounding concrete. To avoid brittle failure, fibre pull-out has to be the dominating mechanism. Fibre fracture is not desirable. A potential fibre rupture depends mainly on the fibre strength, matrix strength, embedment length, fibre geometry and the inclination angle to the crack plane.
Obviously, it is of major importance to choose a suitable fibre-concrete combination to minimize the probability for fibre rupture and at the same time keep the adhesion high enough to ensure a sufficient residual strength after cracking. Pull-out tests are fundamental to characterize the behaviour of FRC, and can be used to optimise the fibre-matrix combination.
Together with knowledge about the orientation and distribution of fibres,
the pull out tests can also be used to estimate the average tension over a crack in a structure. A number of models are developed for this purpose, and one of them will be briefly presented later in this section.
The pull-out process is simplified divided into different stages where the following mechanisms are governing [Robins et al 2002]:
1) Mechanical adhesion as a shear bond at the fibre-matrix interface (bonded phase)
2) Frictional shear bond along the fibre-matrix interface when the fibre slips from the matrix (de-bonded phase)
The mechanical bond is the governing mechanism at very small pull-out lengths, up to a few micrometres [Dupont 2003]. Since the material at the interface zone is less hard than the surrounding bulk material due to higher porosity, very fine cracks spread at a small distance (20-50 μm) from the fibre in the de-bonding phase [Markovic 2006]. At larger pull-out lengths the second mechanism, friction, takes over. Since the displacements in the first stage are ignorable compared to the second stage, the general cohesive interface models are based on a perfectly bonded – de-bonded behaviour.
With this assumption, the pull-out force can reach a critical value without any pull-out displacement taking place. Beyond this critical force, the frictional pull-out in the de-bonded phase takes over. With deformed fibres a third mechanism is introduced:
3) Mechanical anchorage creating localised load transfer points between the fibre and matrix [Robins et al 2002].
For hooked fibres the pull-out behaviour is dominated by the mechanical anchorage. Through the pull-out process, the hooked end has to be deformed into a straight end, provided that concrete spalling or fibre fracture is prevented [Figure 2.12]. Since hooked end steel fibres are used in all experiments carried out and discussed in this thesis, the effect of mechanical anchorage is emphasized in the test methods and models described in this chapter.
Figure 2.12: Typical pull-out response for hooked-end steel fibres, de- bonding and pull-out phases
Figure 2.13: Double side specimen for pull-out test [Robins et al 2002].
First, a fibre is cast in a high strength mortar. Thereafter the test matrix is cast to embed the protruding fibre. The two concrete specimens, connected by the fibre, are then pulled from each other.
Pull-out tests can either be preformed on a group of fibres or on single fibres, and several models and test setups are in use. The pull-out test can
be preformed both on double- and single side specimens. Different test methods for fibre pull-out are described by Patrik Groth [Groth 2002a]. An example of a pull-out test well suited for hooked-end steel fibres is illustrated in Figure 2.13 [Robins et al 2002]. The test is adapted to different embedment lengths and angles. For inclined fibres, it is a major advantage to use a double side specimen, since force is directed in a way that is more true to the real pull-out behaviour in cracked concrete.
Constitutive relation – modelling the pull-out behaviour
Extensive studies have been carried out in order to model the pull-out behaviour of fibres. Two fundamentally different approaches were developed in the 80’s to identify the bond parameters, the stress approach [Nammur and Naaman (1989)] and the fracture mechanical approach [Stang and Shah (1986); Gao (1987); Morrison et al (1988)]. Both approaches describe the pull-out behaviour of a single straight fibre embedded perpendicular to the crack surface.
In the first approach, a general stress-based equation is developed for a perfectly bonded – de-bonded material, where the criterion for growth of the de-bonded fibre/matrix interface is expressed in terms of interfacial stress. At a certain de-bonded length, the shear stress has a maximal value where the de-bonded zone ends. By combining an equation for the maximal shear stress and an expression for the displacement the total fibre displacement versus pull-out load can be determined numerically. A detailed calculation can be found in [Stang, Li, Shah (1990)]. The model gives a good approximation of the material behaviour, but it is rather complex, primarily because some of the input parameters have to be determined from complicated fibre pull-out tests. [Dupont 2003].
In the fracture mechanical approach, the criterion for interfacial de-bonding is expressed in terms of energy equilibrium [Stang, Li, Shah 1990]. As opposed to the stress based model, an analytical solution is possible with the fracture mechanical approach, but also here the extensive input parameters put a limit on the practical use of the model.
The average tension over a crack in a structure can be estimated from single fibre pull-out tests. The individual stresses carried by each fibre with different embedment lengths and angles are then summed and divided by the area of the crack plane. [Dupont 2003]. Models developed for averaging are developed by Balaguru and Shah (1992), Van Gysel (2000) and Stang and Li (2005) among others. The fibre bridging stress versus crack-opening relation σf(δ) can generally be expressed:
( )
10 ~
1 ~ ~
0
( , ) ( ) cos ( )
e
f e
f e
f L
V P L g p dL d
A
φ φ
σ δ δ φ φ φ φ
=
=
∫ ∫
[Stang and Li 2005]where
Vf and Af is the volume and cross-section area of the fibres, φ is the inclination angle,
P(δ,Le) is the single fibre bridging force [Lin, Kanda and Li (1999)],
g(φ) is a function for the normalized load and inclination angle, which may be obtained analytically or from data fit to experiments and
p(φ) is a probability density function.
Fiber pull-out behaviour – conclusions from experiments carried out
Several factors have to be considered when transforming the stress-crack width relation from a single pull-out test to an average stress for a group of fibres with different orientation and embedment lengths crossing a crack. In addition to fibre and matrix properties, the following parameters affect the pull-out behaviour:
– Matrix spalling: If the embedment length is too short, the hook, together with the surrounding matrix is pulled out. To incorporate this into the calculation, the stress in the fibre should be put equal to zero if the initial embedment length becomes smaller than a certain fraction of the fibre length.
– Ineffective anchorage: Even when matrix spalling is avoided, a fibre with end hook will not be fully effective unless the hook is straightened, and it will not be straightened if the embedment length is too short.
– Inclined fibres: The toughness of hooked end and straight fibres has been shown to maximise at a non-zero inclination angle, typically between 15-40 degrees [Robins et al 2002]. This is mainly due to the snubbing effect which results in a higher pull-out force [Dupont 2003].
Snubbing effect causes the fibre segments bridging a crack to remain essentially normal to the crack plane as the crack opens [Stang and Li 2005], but at a certain limit other mechanisms are introduced; the concrete will get a local spalling and the fibre bends. Spalling often follows snubbing because of the high concentrated load where the fibre is forced to bend [Dupont 2003], illustrated in Figure 2.14. Another observation with regard to inclined fibres is that the pull-out response becomes increasingly less influenced by matrix strength and increasingly more influenced by the mechanical properties of the fibre as the inclination to the concrete crack surface increases [Robins et al 2002]. This is due to the snubbing effect; the fibre attempts to straighten in line with the direction of loading, and so inclined pull-out is often associated with yielding of the fibres. Hence, the snubbing effect also leads to higher probability for fibre-rupture. The behaviour of synthetic fibres in pull-out is similar. The pull-out resistance increases with increasing angle due to snubbing, but unlike steel fibre, the additional force due to fibre bending is negligible for synthetic fibres as a result of their low bending stiffness. As for steel fibres, the probability for matrix spalling increases with increasing inclination, and so the strength of the cement matrix influences the pull-out resistance at high angles. Another observation from experiments carried out is that the scatter in the data increases at inclination angles. [Li Wang and Backer 2006]
– Spacing between fibres: When the fibres are very close to each other in a group it can happen that a part of the concrete breaks off, especially with hooked end fibres [Dupont 2003]. This reduces the efficiency of the fibres considerably. The risk of concrete pieces breaking off increases with increasing fibre content.
– Fibre pre-stressing: Shrinkage of the test specimens before loading leads to pre-stressing in the fibres. The pre-stressing magnitude is gradually relaxed and diminishes to zero when the fibre is fully de-bondend. It
decreases rapidly with increasing crack-width and becomes negligible beyond 100μm. [Stang and Li 2005]
– Cook-Gordon effect: When a crack propagates normally towards a fibre, de-bonding occurs between the fibre and matrix. This happens before the crack actually reaches the fibre since the maximum tensile stress is located at a distance ahead of the matrix crack. The so called Cook- Gordon effect creates an additional crack-opening that should be accounted for. [Stang and Li 2005]
Figure 2.14: Spalling often follows snubbing because of high concentrated load where the fibre is forced to bend.
To be able to adopt a good fibre-matrix combination, it is important to be aware of all the above mentioned basic mechanisms of fibre pull-out. But for practical applications, it appears to be too time- and cost consuming to determine all of the parameters needed to calculate a comprehensive constitutive relation, like the approaches developed by Stang, Li & Shah (1990), [Balaguru & Shah 1992, Stang & Li 2001, Van Gysel 2000]. And even if these preliminary tests and calculations are carried out, the natural variations in the material may still result in an inaccurate estimate of the behaviour during failure in the actual structure. Since practical use of FRC is emphasized in this thesis, a more simple approach is presented in the next section.
Test method: Pull-out tests on single fibres [Thorenfeldt et al 2006]
The test method presented here is part of the Norwegian design rule draft for steel fibre reinforced concrete [Thorenfeldt et al. 2006]. Through this procedure, the anchorage capacity of single steel fibres in concrete is determined, dependent on the type of fibre, anchor-length and concrete strength. The load-deformation relation through pull-out is used to establish the characteristic maximal stress and expected average stress in the steel fibres after crack formation.
Figure 2.15: Test setup
Cylindrical concrete specimens (diameter = 100 mm and height = 60 mm) with one single fibre partly cast in perpendicular and centric to the concrete surface are placed in a test rig, as shown in figure Figure 2.15. A gripping device is fixed to the protruding fibre, and the fibre is pulled out of the concrete with a constant deformation of 0.2 mm/min up to a deformation of
LVDT Gripping device
Cast in fibre
Concrete cylinder
